This is a single-center phase two trial evaluating the efficacy of Amifostine in patients receiving agressive chemotherapy with the DICEP regimen. Amifostine is an antioxidant drug which has been shown to affect apoptosis and survival of hematopoietic progenitor cells. This drug has been shown to protect renal and neurologic tissue from the effects of chemotherapy and there is substantial data suggesting that it may also lessen the impact of chemotherapy upon hematopoiesis. Many patients with malignancies such as non-Hodgkin's lymphoma, Hodgkin's disease, and breast cancer, who otherwise might benefit from dose-intensive chemotherapy, are not eligible because of a lack of collectible stem cells. This trial will seek to determine whether amifostine can sufficiently protect hematopoietic progenitor and stem cells during high-dose chemotherapy to allow the administration of dose-intensive therapy without peripheral blood or bone marrow stem cells. We seek to accrue 20 patients.